evaluating logs

May 2010
26
0
i can't seem to get the right answer for this one..

log(base 2) 8root2
(sorry i don't know how to show this on the computer)

the answer in the back of the book is 7/2 but i am getting 3/2
what am i missing?

2^x = 8root2
2^x = 8^1/2
2^x = (2^3)^1/2
2^x = 2^3/2
x=3/2
 

skeeter

MHF Helper
Jun 2008
16,216
6,764
North Texas
i can't seem to get the right answer for this one..

log(base 2) 8root2
(sorry i don't know how to show this on the computer)

the answer in the back of the book is 7/2 but i am getting 3/2
what am i missing?

2^x = 8root2
2^x = 8^1/2
2^x = (2^3)^1/2
2^x = 2^3/2
x=3/2
\(\displaystyle \log_2(8\sqrt{2}) = \log_2(8) + \log_2(\sqrt{2}) = 3 + \frac{1}{2}\)